{"id":"https://openalex.org/W7172272250","doi":"https://doi.org/10.48550/arxiv.2607.28674","title":"How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories","display_name":"How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories","publication_year":2026,"publication_date":"2026-07-28","ids":{"openalex":"https://openalex.org/W7172272250","doi":"https://doi.org/10.48550/arxiv.2607.28674"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.28674","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.28674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.28674","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090509006","display_name":"Hui Wei","orcid":"https://orcid.org/0000-0002-8963-6798"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei, Hui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144252249","display_name":"Junda Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Junda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111520079","display_name":"Shuying Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Sheldon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144300655","display_name":"Sizhe Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Sizhe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064060066","display_name":"Yizhu Jiao","orcid":"https://orcid.org/0000-0003-0509-8652"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiao, Yizhu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144287917","display_name":"Ming Zhong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhong, Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144272313","display_name":"Bowen Jin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Bowen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144284642","display_name":"Tong Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Tong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050975451","display_name":"Shijia Pan","orcid":"https://orcid.org/0000-0002-3226-2318"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pan, Shijia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144270769","display_name":"Jiawei Han","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Han, Jiawei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5144264033","display_name":"Julian McAuley","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"McAuley, Julian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.3018999993801117,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.3018999993801117,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11431","display_name":"Action Observation and Synchronization","score":0.09719999879598618,"subfield":{"id":"https://openalex.org/subfields/3207","display_name":"Social Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.06639999896287918,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.7766000032424927},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.47110000252723694},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4602000117301941},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.37049999833106995},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.33320000767707825},{"id":"https://openalex.org/keywords/visual-reasoning","display_name":"Visual reasoning","score":0.32600000500679016},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.29429998993873596},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.29249998927116394}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.7766000032424927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6349999904632568},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49720001220703125},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.47110000252723694},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4602000117301941},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C2777508537","wikidata":"https://www.wikidata.org/wiki/Q7936620","display_name":"Visual reasoning","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3240000009536743},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.31850001215934753},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.29429998993873596},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.29249998927116394},{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C89288958","wikidata":"https://www.wikidata.org/wiki/Q7301504","display_name":"Reasoning system","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C83725634","wikidata":"https://www.wikidata.org/wiki/Q7268699","display_name":"Qualitative reasoning","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C739882","wikidata":"https://www.wikidata.org/wiki/Q3560506","display_name":"Anomaly detection","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.27160000801086426},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C86827895","wikidata":"https://www.wikidata.org/wiki/Q7098582","display_name":"Opportunistic reasoning","level":4,"score":0.2547999918460846},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.25130000710487366},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.28674","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.28674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.28674","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.28674","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.593555748462677,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Understanding":[0],"how":[1],"computational":[2],"effort":[3,34,47],"is":[4,114],"allocated":[5],"across":[6,67,117],"individual":[7,52],"chain-of-thought":[8],"(CoT)":[9],"reasoning":[10,103,112,135],"steps":[11,54],"remains":[12],"an":[13],"open":[14],"challenge:":[15],"existing":[16],"interpretability":[17],"methods":[18],"rely":[19],"on":[20],"output-level":[21],"signals":[22],"or":[23,79,141],"collapse":[24],"processing":[25],"depth":[26],"into":[27],"a":[28,42],"single":[29],"trajectory-level":[30,125],"scalar,":[31],"leaving":[32],"step-wise":[33],"opaque.":[35],"We":[36],"propose":[37],"Step-Aware":[38],"Reasoning":[39],"Energy":[40],"(SARE),":[41],"geometric":[43,152],"framework":[44],"that":[45,111,150],"quantifies":[46],"at":[48,133],"the":[49],"granularity":[50],"of":[51,63],"CoT":[53,93],"via":[55],"Centered":[56],"Kernel":[57],"Alignment":[58],"(CKA)":[59],"between":[60],"Gram":[61],"matrices":[62],"token":[64],"hidden":[65],"states":[66],"adjacent":[68],"transformer":[69],"layers,":[70],"capturing":[71],"inter-token":[72],"relational":[73],"structure":[74],"without":[75],"requiring":[76],"eigenvector":[77],"alignment":[78],"cluster":[80],"correspondence.":[81],"SARE":[82],"further":[83],"contextualizes":[84],"this":[85],"energy":[86,113,132],"within":[87],"reasoning's":[88],"semantic":[89,99],"progression":[90],"by":[91],"modeling":[92],"trajectories":[94,128],"as":[95],"transitions":[96,122],"among":[97],"latent":[98],"states.":[100],"Across":[101],"six":[102],"benchmarks":[104],"and":[105,137],"three":[106],"open-weight":[107],"LLMs,":[108],"we":[109],"find":[110],"highly":[115],"non-uniform":[116],"step":[118],"types,":[119],"exhibiting":[120],"phase-like":[121],"invisible":[123],"to":[124],"metrics;":[126],"incorrect":[127],"show":[129],"systematically":[130],"lower":[131],"critical":[134],"junctions;":[136],"SARE-based":[138],"features":[139],"match":[140],"outperform":[142],"output-based":[143],"confidence":[144],"baselines":[145],"in":[146],"most":[147],"settings,":[148],"indicating":[149],"internal":[151],"dynamics":[153],"encode":[154],"predictive":[155],"information":[156],"beyond":[157],"surface-level":[158],"signals.":[159]},"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2026-08-04T00:00:00"}
